1.) I've spent a lot of time around costumers who never do "cosplay" (as in dressing up as existing characters). That's the sort of creativity that got me into going to cons in the first place even though I currently do a lot of what they call "re-creations".
History is my biggest inspiration. I'm a bit of a research nut. Honestly, I don't think I'm terribly creative at costume design, though. A lot of my projects revolve around an existing character or idea with an historical bent (like DDR Kabuki).

2.) Not really. Sure, I've done some costumes that are based on another creation of mine (the Red Rebel, which isn't in my gallery at all, for example, is from a comic I drew when I was in high school... and was made in high school). Sure, I've done some like the OP did where you take an idea (aka a DDR game) and turn it into a costume. But do I go and create characters with backstories specifically to cosplay? Not often. The only one I can think of that's not from a fanfic or comic I wrote is the Twelfth Doctor, and that's already based on an existing universe. I didn't plan to create a "backstory", per se, but as I was designing the costume, I thought, What is her personality like? What traits did she pull from past regenerations? which became, How did she regenerate from Smith's Doctor in the first place? Why did she end up female? Who was her companion(s) at the time? And it grew into a story in my head.

3.) Because why not? Costuming hasn't always been about recreating characters. That's relatively new. Costumes are an art form and can be whatever we want them to be. I love love love love love being characters, but sometimes I want to design something new to wear.